Cold-formability of glass laminate article utilizing stress prediction analysis and related methods

ABSTRACT

Articles and methods related to the cold-forming of glass laminate articles utilizing stress prediction analysis are provided. A cold-forming estimator (CFE) value that is related to the stress experienced by a glass sheet of a glass laminate during cold-forming is calculated based on a plurality of geometric parameters of glass layer(s) of a glass laminate article. The calculated CFE value is compared to a cold-forming threshold related to the probability that defects are formed in the complexly curved glass laminate article during cold-forming. Cold-formed glass laminate articles are also provided having geometric parameters such that the CFE value is below the cold-forming threshold.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/667,681 filed on Feb. 9, 2022, which is a continuation of U.S. patentapplication Ser. No. 16/753,972, filed on Apr. 6, 2020, now U.S. Pat.No. 11,261,119, granted Mar. 1, 2022, which is a national stageapplication under 35 U.S.C. § 371 of International Application No.PCT/US2018/054690, filed on Oct. 5, 2018, which claims the benefit ofpriority under 35 U.S.C. § 119 of U.S. Provisional Application Ser. No.62/568,915 filed on Oct. 6, 2017, the contents of which are relied uponand incorporated herein by reference in their entireties.

BACKGROUND

The disclosure relates to cold-formed glass laminate articles, and moreparticularly to articles and methods related to the cold-forming ofglass laminate articles utilizing stress prediction analysis. Inspecific embodiments, such articles may be used for vehicleapplications, such as automotive glazing, and for architecturalapplications.

Curved laminates are used in a variety of applications includingautomotive glazing and architectural windows. For such applications,sheets of glass are precisely bent to defined shapes and/or curvaturesdetermined by the configurations and sizes of the openings in which theglass will be mounted, as well as the vehicle style or architecturalaesthetics. Such curved laminates may typically be made by heating flatglass sheets to a suitable temperature for forming, applying forces tothe sheet to change the shape, then laminating two curved sheetstogether. This process is typically referred to as a “hot bending”process.

SUMMARY

A first aspect of this disclosure pertains to a method of estimatingcold-formability of a complexly curved glass laminate article comprisinga first glass sheet and a second glass sheet. The method includesobtaining a first geometric parameter (G1) and a second geometricparameter (G2) of a complexly curved first glass sheet of the glasslaminate article. The method includes calculating a cold-formingestimator (CFE) value related to stress experienced by the first glasssheet during cold-forming. The CFE value includes B1*G1+B2*G2, where B1and B2 are coefficients calculated to relate G1 and G2 to the CFE value.The method includes comparing the calculated CFE value to a cold-formingthreshold related to the probability that defects are formed in thecomplexly curved glass laminate article during cold-forming.

A second aspect of this disclosure pertains to a method of cold-forminga complexly curved glass laminate article. The method includessupporting a first glass sheet, and the first sheet of glass materialhas a complexly curved shape, a first major surface and a second majorsurface. The method includes supporting a second glass sheet on thefirst glass sheet, and the second glass sheet has a first major surface,a second major surface and a shape that is different from the complexlycurved shape. The method includes positioning a polymer interlayermaterial between the second major surface of the first glass sheet and afirst major surface of the second glass sheet. The method includesbending the second sheet of glass material into conformity with thecomplexly curved shape of the first sheet of glass material. Duringbending, a maximum temperature of the first glass sheet is less than aglass transition temperature of a glass material of the first glasssheet, and a maximum temperature of the second glass sheet is less thana glass transition temperature of a glass material of the second glasssheet. The complexly curved shape has a first geometric parameter (G1)and a second geometric parameter (G2), and the first principle stressexperienced by the first glass sheet during bending is less than orequal to an estimated stress value of (B1*G1+B2*G2), wherein B1 and B2are coefficients determined to relate G1 and G2 to the stressexperienced by the first glass sheet during bending.

Another aspect of the disclosure pertains to a cold-formed glasslaminate article. The glass laminate article includes a first glasslayer and a second glass layer. The first glass layer includes an innersurface, an outer surface opposite the inner surface, a width, W, alength, L, and a complex curved shape having a chord height, CH, where−0.14<L/W−0.05*(CH)<0.223. The second glass layer includes an innersurface and an outer surface. The glass laminate article includes apolymer interlayer disposed between the inner surface of the first glasslayer and inner surface of the second glass layer.

Another aspect of the disclosure pertains to a cold-formed glasslaminate article. The glass laminate article includes a first glasslayer and a second glass layer. The first glass layer includes an innersurface, an outer surface opposite the inner surface, a width, W, alength, L, and an average thickness, T1. The first glass layer includesa complex curved shape having a chord height, CH, a depth of bend (DOB),a minimum primary radius of curvature, R1, a secondary minimum radius ofcurvature, R2, and a maximum Gaussian curvature, GC. The second glasslayer includes an inner surface, an outer surface and an averagethickness, T2. The glass laminate article includes an interlayerdisposed between the inner surface of the first glass layer and innersurface of the second glass layer. The dimensions of the glass laminatearticle are such that(0.05673*W−0.1035*L−0.0031*DOB+6.99003*CH+0.1855*R1+0.00115*R2+4.633988*GC−0.1836*T1−101.95*T2)is less than 80 MPa.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiment(s), and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of a flat glass layer, a curved glasslayer and an intervening film layer before shaping, according to anexemplary embodiment.

FIG. 2 is a cross-sectional view of a glass laminate article formed to acurved shape from the layers shown in FIG. 1 , according to an exemplaryembodiment.

FIG. 3 is a perspective view of a glass laminate article shaped as awindshield, according to an exemplary embodiment.

FIG. 4 is a top plan view of the glass laminate article of FIG. 3 .

FIG. 5 is a perspective view of a glass laminate article shaped as aroof, according to an exemplary embodiment.

FIG. 6 is a top plan view of the glass laminate article of FIG. 5 .

FIG. 7 is a perspective view of a glass laminate article shaped as aside window, according to an exemplary embodiment.

FIG. 8 is a top plan view of the glass laminate article of FIG. 7 .

FIG. 9 shows a process for estimating cold-formability of a complexlycurved glass laminate article, according to an exemplary embodiment.

FIG. 10 shows a comparison of the CFE value calculated using Equation 3for 29 different designs for glass laminate article 50 relative to thecorresponding FEA calculated stresses.

FIGS. 11A and 11B are 2D plots of data from FIG. 10 showing the relationbetween select geometric parameters and cold-forming thresholds.

FIGS. 12A-12C are 2D plots of data from the glass laminate articles ofFIG. 10 designed for windshields.

FIGS. 13A-13C are 2D plots of data from the glass laminate articles ofFIG. 10 designed for roofs.

FIGS. 14A-14C are 2D plots of data from the glass laminate articles ofFIG. 10 designed for side windows (e.g., sidelights).

FIG. 15 is a vehicle equipped with one or more glass laminate articlesas discussed herein.

DETAILED DESCRIPTION

Referring generally to the figures, various methods related tocold-forming a complexly curved glass laminate article. In general,Applicant has determined that a stress (e.g., the first principlestress) experienced by one or more of the glass layers of a glasslaminate during cold-bending is a good indicator of the likelihood ofdefect formation during cold bending. For example, Applicant has foundthat if the cold-bending stress experienced during cold-bending is toohigh, defects, such as edge wrinkling, or breakage can occur. However,standard processes, such as finite element analysis, to preciselycalculate the stress that a glass laminate article will experienceduring cold bending are complicated and take substantial amounts ofcomputing time and power.

As such, the present application relates to a process of determiningcold-formability of glass laminate articles by calculating acold-forming estimator (CFE) value that is related to the stress thatglass sheet is expected to experience during cold-forming. The CFE valueis then compared to a cold-forming threshold that is related to theprobability that defects will be formed in the complexly curved glasslaminate article during cold-forming. The CFE value is based on the sumof at least two geometric parameters indicative of the geometry of theglass laminate article that each are multiplied by statisticallycalculated coefficients. The cold-forming threshold may be determinedvia testing of different laminate structures to determine a thresholdvalue that relates to a maximum acceptable stress that may beexperienced by the glass laminate article during cold-bending without anundesired level defect formation.

Using the method discussed herein, once the CFE coefficients aredetermined and the cold-forming threshold is determined, defectformation during cold-forming can be accurately predicted simply bycalculating the CFE value based on easy to measure geometric parametersof the glass laminate article. As such the method discussed hereineliminates the need for running complex mathematical analysis (e.g.,finite element analysis) or prototyping/testing to determine whether anew complexly curved glass laminate article design may be cold-formedwithout unacceptable defect formation. Thus, in this manner the processof cold-forming new, complexly curved glass laminate articles may bestreamlined.

Referring to FIG. 1 and FIG. 2 , a cold-formed glass laminate articleand a formation process are shown according to exemplary embodiments. Asshown in FIG. 1 , a laminate stack 10 includes a first glass layer 12having a complexly curved shape. First glass layer 12 includes an outersurface 14 that includes at least one section that has a convex shape,and an inner surface 16 is opposite outer surface 14 and includes atleast one section having a concave shape. A thickness, such as anaverage thickness T1, is defined between outer surface 14 and innersurface 16.

Laminate stack 10 also includes a second glass layer 20. Glass layer 20includes an outer surface 22 and an inner surface 24 opposite of outersurface 22. A thickness, such as an average thickness T2, is definedbetween outer surface 22 and inner surface 24. In some embodiments,glass layer 20 is thinner than glass layer 12 such that T1>T2, and inspecific embodiments, the glass material composition of glass layer 12is different from the glass material composition of glass layer 20. Invarious embodiments, T1 is at least 2.5 times greater than T2, and inother embodiments, T2 is at least 2.5 times greater than T1. In specificembodiments, T1 is between 1.5 mm and 4 mm, and T2 is between 0.3 mm and1 mm, and in even more specific embodiments, T2 is less than 0.6 mm. Inspecific embodiments: T1 is 1.6 mm and T2 is 0.55 mm; T1 is 2.1 mm andT2 is 0.55 mm; T1 is 2.1 mm and T2 is 0.7 mm; T1 is 2.1 mm and T2 is 0.5mm; T1 is 2.5 mm and T2 is 0.7 mm.

Laminate stack 10 includes an interlayer 30 positioned between firstglass layer 12 and the second glass layer 20. In this arrangement,interlayer 30 is located between inner surface 16 of first glass layer12 and inner surface 24 of second glass layer 20. In specificembodiments, the interlayer 30 is affixed to at least one of innersurface 16 of first glass layer 12 and inner surface 24 of second glasslayer 20 and acts to hold together laminate 50 following formation(shown in FIG. 2 ). Interlayer 30 may be a polymer interlayer such as apolyvinyl butyral layer.

FIG. 1 illustrates a cross-sectional view of laminate stack 10 beforecold-forming, and FIG. 2 illustrates a glass laminate article, laminate50, formed from laminate stack 10 via cold-forming. As shown in FIG. 1 ,first glass layer 12 is supported (e.g., on a frame), and second glasslayer 20 is positioned to be supported on first glass layer 12. Polymerinterlayer 30 is positioned between first glass layer 12 and secondglass layer 20.

As shown in FIG. 1 , first glass layer 12 is formed in a curved shapeprior to beginning of the cold-forming process, and second glass layer20 is flat prior to the forming process. During the cold-forming processof FIG. 1 , pressure, shown by the arrows P, is applied to the stacksuch that the second glass layer 20, interlayer 30, and first glasslayer 12 are pressed together. Under pressure P, second glass layer 20deforms to take on the curved shape of first glass layer 12, and oncesecond glass layer 20 has been shaped to match the shape of first glasslayer 12, first glass layer 12 and second glass layer 20 are bondedtogether by the interlayer 30, forming the complexly curved article 50,shown in FIG. 2 .

As can be seen in FIG. 2 following shaping, second glass layer 20 alsohas a curved shape such that outer surface 22 includes at least onesection that has a concave shape and that inner surface 24 includes atleast one section having a convex shape. The shaping process shownensures that the shape and curvature of second glass layer 20 closelymatches the shape and curvature of first glass layer 12. Thus, in thisarrangement, second glass layer 20 is bent to conform to the complexcurved shape of first glass layer 12 via pressure P, without thetemperature being raised above the glass transition temperature of theglass material of second glass layer 20 and/or of the glass material offirst glass layer 12.

In various embodiments, the shaping pressure, represented by arrows Pmay be about 1 atmosphere or greater. The shaping pressure may be airpressure and/or pressure applied via a press or die.

In various embodiments, first glass layer 12 is formed to its complexlycurved shape via a hot forming process, and then is cooled prior to thecold-forming process shown in FIG. 1 . In specific embodiments, hotforming first glass layer 12 may include heating it to a temperaturenear the softening point of the glass material of first glass layer 12and then bending it to the complexly curved shape.

During the forming process of FIG. 1 , the complexly curved first glasslayer 12 and the flat second glass layer 20 are cold-formed into thecurved laminate 50 at a temperature well below the softening point ofthe glass material of second glass layer 20 and/or of the glass materialof first glass layer 12. In various embodiments, the cold-formingprocess of FIG. 1 occurs at a temperature that is 200 degrees C. or morebelow the softening point of the glass material of second glass layer 20and/or of the glass material of first glass layer 12. Softening pointrefers to the temperature at which glass will deform under its ownweight. In one or more specific embodiments, the temperature during thecold-forming process is below about 400 degrees C., below about 350degrees C., or below about 300 degrees C. In one specific embodiment thecold-forming process is in the range of room temperature to about 140degrees C. C Room temperature can be considered to be the ambienttemperature of a production floor (e.g., 16 degrees C. to about 35degrees C.).

As shown in FIG. 1 , interlayer 30 is located between glass layers 12and 20 during cold-forming. In some such embodiments, interlayer 30 actsto bond together glass layers 12 and 20 before or during cold forming.In some such embodiments, stack 10 is heated to a temperature in therange of about 100 degrees C. to about 140 degrees C. during applicationof pressure P in order to form a bond between interlayer 30 and glasslayers 12 and 20.

As shown in FIGS. 3-8 , in various embodiments, laminate 50 is shownshaped into a variety of complex curved shapes to illustrate variousgeometric parameters that may be used to determine a CFE value. As shownin FIGS. 3-8 , geometric parameters of first glass layer 12 that may beutilized to calculate the CFE value may include a width, W, a length, L,a chord height, CH, a depth of bend (DOB), a minimum primary radius ofcurvature, R1, a secondary minimum radius of curvature, R2, and amaximum Gaussian curvature, GC. In specific embodiments, determinationof the CFE value may also include additional geometric parameters suchas thickness, T1, of first glass layer 12 and thickness, T2, of secondglass layer 20.

As shown in FIGS. 3-8 , glass laminate article 50 may be shaped into avariety of shapes for a wide variety of applications. For example, FIGS.3-4 show glass laminate article 50 shaped to form an automotivewindshield according to an exemplary embodiment. FIGS. 5-6 show glasslaminate article 50 shaped to form an automotive roof/sunroof/moon roofaccording to an exemplary embodiment. FIGS. 7-8 show glass laminatearticle 50 shaped to form an automotive side window (e.g., a sidelight)according to an exemplary embodiment.

As can be seen in FIGS. 3-8 , it may be desirable for glass laminatearticle 50 to be shaped into a wide variety of complexly curved shapesas may be needed for a particular application, vehicle body design, etc.Typically, to determine whether a particular glass laminate articledesign is suitable for cold-forming, complicated and processingintensive finite element analysis (FEA) would need to be conducted todetermine whether stresses within the glass layers during cold-bendingwould be too high and thus cause defects. Because of the large number ofpotential article shapes and designs and the need for fast production,Applicant has developed a process for predicting whether a glasslaminate article shape is suitable for cold-forming utilizing arelatively simple calculation that does not rely on FEA or othercomputer modeling techniques.

Further, FIGS. 3-8 illustrate different geometric parameters that may beused to calculate a CFE value as discussed herein. As shown in FIGS. 3-8, glass laminate article 50 (or one of the glass layers of article 50)includes a width, W, a length, L, a chord height, CH, a depth of bend(DOB), a minimum primary radius of curvature, R1, a secondary minimumradius of curvature, R2, and a maximum Gaussian curvature, GC. As shownin FIG. 1 glass layers 12 and 20 also have average thicknesses, T1 andT2. In the specific embodiments discussed herein, these dimensions aredefined as follows: width, WI, is the width of a minimum bounding boxcontaining the glass laminate article 50; length, L1, is the length of aminimum bounding box containing glass laminate article 50; depth ofbend, DOB, is the maximum depth of glass laminate article 50 from theprojection plane; chord height, CH, is the maximum perpendiculardistance between the center line chord and the arc of the glass surfaceof glass laminate article 50; a minimum primary radius of curvature, R1,is the minimum radius along primary bending curvature direction;secondary minimum radius of curvature, R2, is the minimum radius alongcross bending curvature direction; Gaussian Curvature is the product ofthe principal curvatures at a point, where principal curvatures are theminimum and maximum of the normal curvatures at a point, and normalcurvatures are the curvatures of curves on the surface lying in planesincluding the tangent vector at the given point.

As will be discussed in more detail below, various combinations of thesegeometric parameters are used for a variety of CFE values.

In general, referring to FIG. 9 , the present disclosure provides amethod 100 of estimating cold-formability of a complexly curved glasslaminate article, such as article 50. At step 102, a plurality ofgeometric parameters, such a first geometric parameter (G1) and a secondgeometric parameter (G2), of a complexly curved first glass sheet of theglass laminate article are obtained. As will be discussed below, invarious embodiments, more than two geometric parameters may be utilizedin the cold-formability estimation methods discussed herein. At step104, a cold-forming estimator (CFE) value related to stress experiencedby the first glass sheet during cold-forming is calculated. At step 106,the calculated CFE value is compared to a cold-forming threshold whichis related to the probability that defects will be formed in thecomplexly curved glass laminate article during cold-forming.

In general, the comparison at step 106 is then used to determine whetheror not a particular design for a complexly curved article 50 is suitablefor cold-forming. In specific embodiments, a cold-forming method such asthat discussed above in relation to FIG. 1 is then performed if CFEvalue is less than the cold-forming threshold. Because of thecorrelation between the various CFE values discussed herein and thefirst principle stress experienced by the first glass layer during coldforming, when cold-forming is performed on a glass laminate article thathas a CFE value less than the cold-forming threshold, the stresseswithin glass laminate article 50 during cold-forming remain at a levelthat causes defects.

In general, the CFE value is a summation of two or more geometricparameters associated with glass laminate article 50 (multiplied bycalculated coefficients as discussed herein) which Applicant hasdetermined provide a high level of correlation to stresses experiencedduring cold-forming. Thus, by calculating a CFE value as discussedherein a determination of cold-formability of a particular glasslaminate design can be made without the need to perform FEA for aparticular design or to prototype and test a particular design. Thus,while the CFE value may be calculated in a variety of ways as will bediscussed herein, in one embodiment, the CFE value is B1*G1+B2*G2,wherein B1 and B2 are coefficients calculated using statistical methodsto relate G1 and G2 to the glass laminate article is suitable forcold-forming.

In general, coefficients B1 and B2 (and coefficients for any additionalgeometric parameters that may be used to calculate the CFE value) aredetermined by multiple linear regression analyses of finite elementanalysis-determined stresses of multiple complexly curved glass laminatearticles. Thus, by calculating the linear regression analysis on adataset of FEA determined stresses for multiple complex curved articles,the impact or relation of G1 and G2 (and additional geometric parametersas discussed below) to the stress experienced during cold forming can bedetermined. This analysis provides the value for coefficients B1 and B2to be determined. Once B1 and B2 (and coefficients for any additionalgeometric parameters that may be used to calculate the CFE value) aredetermined, the CFE value can be calculated as the summation of thedesired set of geometric parameters multiplied by the coefficient,without the need to run FEA for each new design evaluated.

Applicant believes that the coefficients, such as B1 and B2, arefunctions of the glass materials of first glass layer 12 and secondglass layer 20. Thus, B1 and B2 (and coefficients for any additionalgeometric parameters that may be used to calculate the CFE value) willbe determined via linear regression analysis for the material types ofthe glass layers of a particular glass laminate article, and then can beused to calculate the CFE value for different sizes, shapes, curvatures,etc. of different laminate designs without conducting FEA for each newdesign.

Further, the cold-forming threshold is also believed to be a function ofthe glass materials of first glass layer 12 and second glass layer 20.In various embodiments, the cold-forming threshold is related to amaximum allowable stress that first glass sheet 12 can experiencewithout defect formation. In specific embodiments, the cold-formingthreshold is determined by evaluating whether defects are present inlaminated test samples of a variety of sizes and shapes, and then bycorrelating the presence or absence of defects to stress levels expectedduring cold bending that are calculated using finite element analysis orthrough measurement. Further, Applicant believes that the cold formingthreshold is a function of the strength of the material of layers 12 and20.

In a specific embodiment, the first geometric parameter, G1, is L/W, thesecond geometric parameter, G2 is the chord height, CH, B1 is 1 andB2=−0.05. Thus in such embodiments, the CFE value is determined by:CFE=L/W−0.05CH)  Equation 1When the value of Equation 1 is less than a determined cold-formingthreshold, a determination is made that the glass laminate articlehaving L, W and CH is cold-formable. In a specific embodiment, when−0.14<(L/W−0.05 CH<0.223, a determination is made that the glass articlehaving L, W and CH is cold-formable, and in such embodiments, a laminateglass article 50 may be formed having a shape and size such that−0.14<L/W−0.05*(CH)<0.223. In some such embodiments, first glass layer12 is formed from a soda lime glass material, and second glass layer 20is formed from an alkali aluminosilicate glass composition or an alkalialuminoborosilicate glass composition.

In another specific embodiment, G1=the chord height, CH, G2=maximumGaussian curvature, GC, B1=1 and B2=1. Thus in such embodiments,CFE=(CH+GC), and when this value is less than a determined cold-formingthreshold, a determination is made that the glass article having GC andCH is cold-formable. In a specific embodiment, when 8<(GC+CH)<20, adetermination is made that the glass article having GC and CH iscold-formable. In some such embodiments, first glass layer 12 is formedfrom a soda lime glass material, and second glass layer 20 is formedfrom an alkali aluminosilicate glass composition or an alkalialuminoborosilicate glass composition.

In another specific embodiment, first glass layer 12 includes a width,W, a length, L, a chord height, CH, a depth of bend (DOB), a minimumprimary radius of curvature, R1, a secondary minimum radius ofcurvature, R2, average thickness, T1, and a maximum Gaussian curvature,GC. In addition, second glass layer 20 includes a thickness, T2. In suchembodiments, the CFE value is a predicted stress value and is determinedby:CFE=B0+B1*W+B2*L+B3*DOB+B4*CH+B5*R1+B6*R2+B7*GC+B8*T1+B9*T2).  Equation2In this embodiment the units for the 9 geometric parameters are asfollows: W (mm), L (mm), DOB (mm), CH (mm), R1 (mm), R2 (mm), themaximum GC in 10⁻⁷ (1/mm²), T1 (mm) and the T2 (mm). The constantcoefficients, B0-B9, for each geometric parameter are determined from anFEA dataset for glass laminate articles 50 having different geometricparameters but formed from the same materials.

In a particular embodiment, B0-B9 were calculated from a data set of FEAdetermined stress for 29 different glass laminate article designs andare as shown in Table 1.

TABLE 1 Width Length DOB Chord H Min. R1 Min. R2 Max. GC T1 T2 (mm) (mm)(mm) (mm) (mm) (mm) (10⁻⁷ mm⁻²) (mm) (mm) β₀ β₁ β₂ β₃ β₄ β₅ β₆ β₇ β₈ β₉0 0.05673 −0.1035 −0.0031 6.99003 0.01855 0.00115 4.633988 −0.1836−101.95

Using this data, Equation 2 becomes:CFE=0.05673*W−0.1035*L−0.0031*DOB+6.99003*CH+0.01855*R1+0.00115*R2+4.633988*GC−0.1836*T1−101.95*T2.  Equation3

Then for a given design of a glass laminate article 50, the value ofEquation 3 is then compared to the cold-forming threshold to determinecold formability. In specific embodiments, utilizing this equation, thecold-forming threshold is 80 MPa, 50 MPa, or 20 MPa. Thus in suchembodiments, a laminate glass article 50 is formed having a shape andsize such that is(0.05673*W−0.1035*L−0.0031*DOB+6.99003*CH+0.01855*R1+0.00115*R2+4.633988*GC−0.1836*T1−101.95*T2)<80MPa.

As will be understood in this embodiment, W, L, CH, DOB, R1, R2, T1 andGC are all geometric parameters of first layer 12, and T2 is a geometricparameter of second glass layer 20. The coefficients shown in Equation 3were determined using linear regression analysis as described above. Insome such embodiments, first glass layer 12 is formed from a soda limeglass material, and second glass layer 20 is formed from an alkalialuminosilicate glass composition or an alkali aluminoborosilicate glasscomposition.

In specific embodiments, first glass layer 12 is formed from anunstrengthened glass sheet, and the cold-forming threshold is determinedto be 20 MPa. In this embodiment, the CFE value is a predicted stressvalue and is given by Equation 3. In such embodiments, the method ofpredicting cold-formability includes determining that a particulardesign for glass laminate article 50 is suitable for cold-forming, whenthe calculated CFE value of Equation 30 is less than the 20 MPa.

In another specific embodiment, first glass layer 12 is formed from astrengthened glass sheet (e.g., a thermally strengthened glass material,a chemically strengthened glass sheet, etc.), and the cold-formingthreshold is determined to be 50 MPa. In this embodiment, the CFE valueis a predicted stress value and is given by Equation 3. In suchembodiments, the method of predicting cold-formability includesdetermining that a particular design for glass laminate article 50 issuitable for cold-forming, when the calculated CFE value of Equation 3is less than the 50 MPa.

In various embodiments, first glass layer 12 is formed from a soda limeglass material, and second glass layer 20 is formed from an alkalialuminosilicate glass composition or an alkali aluminoborosilicate glasscomposition. In some such embodiments, glass layer 20 is chemicallystrengthened via ion exchange. In some embodiments, first glass layer 12may be annealed. In some embodiments, both layers 12 and 20 are formedfrom soda lime glass. In other embodiments, both layers 12 and 20 areformed from an alkali aluminosilicate glass composition or an alkalialuminoborosilicate glass composition.

In various embodiments, W is between 300 mm and 1800 mm, L is between230 mm and 1600 mm, CH is between 1 mm and 45 mm, DOB is between 5 mmand 210 mm, R1 is between 40 mm and 5000 mm, R2 is between 740 mm and32500 mm, GC is between 0.14×10⁻⁷ 1/mm² and 15×10⁻⁷ 1/mm², T1 is between1 mm and 4 mm, and T2 is between 0.3 mm and 1 mm.

To provide further examples, FIGS. 10-14C show the plots of data showingthe relation between various CFE values and various cold-formingthresholds. FIG. 10 shows a comparison of the CFE value calculated usingEquation 3 for 29 different designs for glass laminate article 50 inrelation to the FEA calculated stresses for the designs. As can be seenin FIG. 10 , when the CFE value calculated using Equation 3 is belowcold-forming threshold 120, the FEA determined stress for a particularglass article design is also less than cold forming threshold 120, andthis relation indicates that the article is cold-formable. In thisembodiment, cold-forming threshold 120 is 20 MPa.

As shown in FIG. 10 , an upper cold forming threshold 130 can also bedetermined. As can be seen in FIG. 10 , when the CFE value calculatedusing Equation 3 is above cold-forming threshold 130, the FEA determinedstress for a particular glass article design is also above the coldforming threshold 130, and this indicates that the article is notcold-formable. If the CFE value calculated using Equation 3 is betweenthreshold 120 and threshold 130 the correlation between the calculatedCFE value and the FEA stress value is low, and therefore in this range,FEA stress should be calculated to determine whether or not a particularglass laminate design in this range is cold-formable because thepredictive value of the CFE value is low. In specific embodiments,threshold 130 is based on the B10 values of the material of first glasslayer 12 (soda-lime glass in the specific embodiment shown) based onWeibull distribution, and threshold 120 is determined as the thresholdbelow which the chances of forming wrinkling layer 20 is acceptably low.By way of explanation, during cold forming process, stress builds up onboth layers of a glass laminate article. Typically one of the layers(e.g., the soda-lime glass layer) has a much lower strength compared toother layer (e.g., a chemically strengthened layer). Therefore, theweaker is used to determine the threshold of the strength duringbending.

FIGS. 11A and 11B are 2D plots of data from FIG. 10 showing the relationbetween select geometric parameters and cold-forming thresholds 120 and130. FIG. 11A is a 2D map created using maximum GC and chord height, andFIG. 11B is a 2D map created using chord height, CH, and L/W. Both mapsin FIGS. 11A and 11B are divided into three regions separated bycold-forming thresholds 120 and 130, respectively. Most data points arein the desired region with a few exceptions. FIG. 11A shows a clearcorrelation between the two parameters, max GC and CH: when the chordheight increases, the max GC should be reduced in order to ensure thelaminate article is cold formable. Similarly, FIG. 11B shows a clearcorrelation between the two parameters, L/W and chord height, CH: whenthe chord height increases, L/W needs to increase to make glass laminatearticle cold formable.

FIGS. 12A-12C are 2D plots from the glass laminate articles from FIG. 10designed for windshields. As shown in FIG. 12B, the L/W value for thewindshield designs is mainly distributed over the range of 0-0.8. Thewindshield data has cold forming thresholds 120 and 130 similar to theoverall data in the Max GC-Chord Height plot (FIG. 11A) and L/W-ChordHeight plot (FIG. 11B).

FIGS. 13A-13C are 2D plots from the glass laminate articles from FIG. 10designed for roofs. As shown in FIG. 13B, the L/W value is mainlydistributed over the range of 0-1.0. As shown, the roof data has a widerzone between thresholds 120 and 130 as compared to the overall data(FIGS. 11A and 11B).

FIGS. 14A-14C are 2D plots from the glass laminate articles from FIG. 10designed for side windows (e.g., sidelights). As shown in FIG. 14B, theL/W value is mainly distributed over the range of 0-0.7.

Referring to FIG. 15 , use of glass laminate article 50 as part of avehicle window, roof or side window, is shown. As shown, a vehicle 200includes one or more side window 202, a roof 204, a back window 206and/or a windshield 208. In general, any of the embodiments of glasslaminate article 50 discussed herein may be used for one or more sidewindow 202, a roof 204, a back window 206 and/or a windshield 208. Ingeneral, one or more side window 202, a roof 204, a backwindow 206and/or a windshield 208 are supported within an opening defined byvehicle frame or body 210 such that outer surface 22 of second glasslayer 20 (see FIG. 1 ) faces a vehicle interior 212. In thisarrangement, outer surface 14 of first glass layer 12 (see FIG. 1 )faces toward the exterior of vehicle 200 and may define the outermostsurface of vehicle 200 at the location of the glass article. As usedherein, vehicle includes automobiles, rolling stock, locomotive, boats,ships, airplanes, helicopters, drones, space craft and the like. Inother embodiments, glass laminate article 50 may be used in a variety ofother applications where thin, curved glass laminate articles may beadvantageous, such as for architectural glass, building glass, etc.

As used herein “complex curve” and “complexly curved” mean a non-planarshape having curvature along two orthogonal axes that are different fromone another. Examples of complexly curved shapes includes having simpleor compound curves, also referred to as non-developable shapes, whichinclude but are not limited to spherical, aspherical, and toroidal. Thecomplexly curved laminates according to embodiments may also includesegments or portions of such surfaces, or be comprised of a combinationof such curves and surfaces. In one or more embodiments, a laminate mayhave a compound curve including a major radius and a cross curvature. Acomplexly curved laminate according to embodiments may have a distinctradius of curvature in two independent directions. According to one ormore embodiments, complexly curved laminates may thus be characterizedas having “cross curvature,” where the laminate is curved along an axis(i.e., a first axis) that is parallel to a given dimension and alsocurved along an axis (i.e., a second axis) that is perpendicular to thesame dimension. The curvature of the laminate can be even more complexwhen a significant minimum radius is combined with a significant crosscurvature, and/or depth of bend.

Some laminates may also include bending along axes that are notperpendicular to one another. As a non-limiting example, thecomplexly-curved laminate may have length and width dimensions of 0.5 mby 1.0 m and a radius of curvature of 2 to 2.5 m along the minor axis,and a radius of curvature of 4 to 5 m along the major axis. In one ormore embodiments, the complexly-curved laminate may have a radius ofcurvature of 5 m or less along at least one axis. In one or moreembodiments, the complexly-curved laminate may have a radius ofcurvature of 5 m or less along at least a first axis and along thesecond axis that is perpendicular to the first axis. In one or moreembodiments, the complexly-curved laminate may have a radius ofcurvature of 5 m or less along at least a first axis and along thesecond axis that is not perpendicular to the first axis.

Glass layers 12 and/or 20 can be formed from a variety of materials. Inspecific embodiments, glass layer 20 is formed from a chemicallystrengthened alkali aluminosilicate glass composition or an alkalialuminoborosilicate glass composition, and glass layer 12 is formed froma soda lime glass (SLG) composition. In specific embodiments, glasslayers 12 and/or 20 are formed from a chemically strengthened material,such as an alkali aluminosilicate glass material or an alkalialuminoborosilicate glass composition, having a chemically strengthenedcompression layer having a depth of compression (DOC) in a range fromabout 30 μm to about 90 μm, and a compressive stress on at least one ofthe sheet's major surfaces of between 300 MPa to 1000 MPa. In someembodiments, the chemically strengthened glass is strengthened throughion exchange.

Examples of Glass Materials and Properties

In various embodiments, glass layers 12 and/or 20 may be formed from anyof a variety of glass compositions. Examples of glasses that may be usedfor glass layers 12 and/or 20 described herein may include soda-limesilicate glass compositions, aluminosilicate glass compositions, alkalialuminosilicate glass compositions or alkali aluminoborosilicate glasscompositions, though other glass compositions are contemplated. In oneor more embodiments, suitable glass compositions may be characterized asion exchangeable. As used herein, “ion exchangeable” means that thelayer comprising the composition is capable of exchanging cationslocated at or near the surface of the glass layer with cations of thesame valence that are either larger or smaller in size. In one exemplaryembodiment, the glass composition of glass layers 12 and/or 20 comprisesSiO₂, B₂O₃ and Na₂O, where (SiO₂+B₂O₃)≥66 mol. %, and Na₂O≥9 mol. %.Suitable glass compositions for glass layers 12 and/or 20, in someembodiments, further comprise at least one of K₂O, MgO, and CaO. In aparticular embodiment, the glass compositions used in glass layers 12and/or 20 can comprise 61-75 mol. % SiO₂; 7-15 mol. % Al₂O₃; 0-12 mol. %B₂O₃; 9-21 mol. % Na₂O; 0-4 mol. % K₂O; 0-7 mol. % MgO; and 0-3 mol. %CaO.

A further example of glass composition suitable for glass layers 12and/or 20 comprises: 60-70 mol. % SiO₂; 6-14 mol. % Al₂O₃; 0-15 mol. %B₂O₃; 0-15 mol. % Li₂O; 0-20 mol. % Na₂O; 0-10 mol. % K₂O; 0-8 mol. %MgO; 0-10 mol. % CaO; 0-5 mol. % ZrO₂; 0-1 mol. % SnO₂; 0-1 mol. % CeO₂;less than 50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 12 mol.%≤(Li₂O+Na₂O+K₂O)≤20 mol. % and 0 mol. %≤(MgO+CaO)≤10 mol. %.

Even further, another example of glass composition suitable for glasslayers 12 and/or 20 comprises: 63.5-66.5 mol. % SiO₂; 8-12 mol. % Al₂O₃;0-3 mol. % B₂O₃; 0-5 mol. % Li₂O; 8-18 mol. % Na₂O; 0-5 mol. % K₂O; 1-7mol. % MgO; 0-2.5 mol. % CaO; 0-3 mol. % ZrO₂; 0.05-0.25 mol. % SnO₂;0.05-0.5 mol. % CeO₂; less than 50 ppm As₂O₃; and less than 50 ppmSb₂O₃; where 14 mol. %≤(Li₂O+Na₂O+K₂O)≤18 mol. % and 2 mol.%≤(MgO+CaO)≤7 mol. %.

In a particular embodiment, an alkali aluminosilicate glass compositionsuitable for glass layers 12 and/or 20 comprises alumina, at least onealkali metal and, in some embodiments, greater than 50 mol. % SiO₂, inother embodiments at least 58 mol. % SiO₂, and in still otherembodiments at least 60 mol. % SiO₂, wherein the ratio ((Al₂O₃+B₂O₃)/Σmodifiers)>1, where in the ratio the components are expressed in mol. %and the modifiers are alkali metal oxides. This glass composition, inparticular embodiments, comprises: 58-72 mol. % SiO₂; 9-17 mol. % Al₂O₃;2-12 mol. % B₂O₃; 8-16 mol. % Na₂O; and 0-4 mol. % K₂O, wherein theratio((Al₂O₃+B₂O₃)/Σ modifiers)>1.

In still another embodiment, glass layers 12 and/or 20 may include analkali aluminosilicate glass composition comprising: 64-68 mol. % SiO₂;12-16 mol. % Na₂O; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃; 2-5 mol. % K₂O;4-6 mol. % MgO; and 0-5 mol. % CaO, wherein: 66 mol. % SiO₂+B₂O₃+CaO 69mol. %; Na₂O+K₂O+B₂O₃+MgO+CaO+SrO>10 mol. %; 5 mol. % MgO+CaO+SrO≤8 mol.%; (Na₂O+B₂O₃)—Al₂O₃≤2 mol. %; 2 mol. %≤Na₂O—Al₂O₃≤6 mol. %; and 4 mol.%≤(Na₂O+K₂O)—Al₂O₃≤10 mol. %.

In an alternative embodiment, glass layers 12 and/or 20 may comprise analkali aluminosilicate glass composition comprising: 2 mol % or more ofAl₂O₃ and/or ZrO₂, or 4 mol % or more of Al₂O₃ and/or ZrO₂. In one ormore embodiments, glass layers 12 and/or 20 comprise a glass compositioncomprising SiO₂ in an amount in the range from about 67 mol % to about80 mol %, Al₂O₃ in an amount in a range from about 5 mol % to about 11mol %, an amount of alkali metal oxides (R₂O) in an amount greater thanabout 5 mol % (e.g., in a range from about 5 mol % to about 27 mol %).In one or more embodiments, the amount of R₂O comprises Li₂O in anamount in a range from about 0.25 mol % to about 4 mol %, and K₂O in anamount equal to or less than 3 mol %. In one or more embodiments, theglass composition includes a non-zero amount of MgO, and a non-zeroamount of ZnO.

In other embodiments, glass layers 12 and/or 20 are formed from acomposition that exhibits SiO₂ in an amount in the range from about 67mol % to about 80 mol %, Al₂O₃ in an amount in the range from about 5mol % to about 11 mol %, an amount of alkali metal oxides (R₂O) in anamount greater than about 5 mol % (e.g., in a range from about 5 mol %to about 27 mol %), wherein the glass composition is substantially freeof Li₂O, and a non-zero amount of MgO; and a non-zero amount of ZnO.

In other embodiments, glass layers 12 and/or 20 are an aluminosilicateglass article comprising: a glass composition comprising SiO₂ in anamount of about 67 mol % or greater; and a sag temperature in a rangefrom about 600° C. to about 710° C. In other embodiments, glass layers12 and/or 20 are formed from an aluminosilicate glass articlecomprising: a glass composition comprising SiO₂ in an amount of about 68mol % or greater; and a sag temperature in a range from about 600° C. toabout 710° C. (as defined herein).

In some embodiments, glass layers 12 and/or 20 are formed from differentglass materials from each other that differs in any one or more ofcomposition, thickness, strengthening level, and forming method (e.g.,float formed as opposed to fusion formed). In one or more embodiments,glass layers 12 and/or 20 described herein have a sag temperature ofabout 710° C., or less or about 700° C. or less. In one or moreembodiments, one of the glass layers 12 and 20 is a soda lime glasssheet, and the other of the glass layers 12 and 20 is any one of thenon-soda lime glass materials discussed herein. In one or moreembodiments, glass layers 12 and/or 20 comprises a glass compositioncomprising SiO₂ in an amount in the range from about 68 mol % to about80 mol %, Al₂O₃ in an amount in a range from about 7 mol % to about 15mol %, B₂O₃ in an amount in a range from about 0.9 mol % to about 15 mol%; a non-zero amount of P₂O₅ up to and including about 7.5 mol %, Li₂Oin an amount in a range from about 0.5 mol % to about 12 mol %, and Na₂Oin an amount in a range from about 6 mol % to about 15 mol %.

In some embodiments, the glass composition of glass layers 12 and/or 20may include an oxide that imparts a color or tint to the glass articles.In some embodiments, the glass composition of glass layers 12 and/or 20includes an oxide that prevents discoloration of the glass article whenthe glass article is exposed to ultraviolet radiation. Examples of suchoxides include, without limitation, oxides of: Ti, V, Cr, Mn, Fe, Co,Ni, Cu, Ce, W, and Mo.

Glass layers 12 and/or 20 may have a refractive index in the range fromabout 1.45 to about 1.55. As used herein, the refractive index valuesare with respect to a wavelength of 550 nm. Glass layers 12 and/or 20may be characterized by the manner in which it is formed. For instance,glass layers 12 and/or 20 may be characterized as float-formable (i.e.,formed by a float process), down-drawable and, in particular,fusion-formable or slot-drawable (i.e., formed by a down draw processsuch as a fusion draw process or a slot draw process). In one or moreembodiments, glass layers 12 and/or 20 described herein may exhibit anamorphous microstructure and may be substantially free of crystals orcrystallites. In other words, in such embodiments, the glass articlesexclude glass-ceramic materials.

In one or more embodiments, glass layers 12 and/or 20 exhibits anaverage total solar transmittance of about 88% or less, over awavelength range from about 300 nm to about 2500 nm, when glass layers12 and/or 20 has a thickness of 0.7 mm. For example, glass layers 12and/or 20 exhibits an average total solar transmittance in a range fromabout 60% to about 88%, from about 62% to about 88%, from about 64% toabout 88%, from about 65% to about 88%, from about 66% to about 88%,from about 68% to about 88%, from about 70% to about 88%, from about 72%to about 88%, from about 60% to about 86%, from about 60% to about 85%,from about 60% to about 84%, from about 60% to about 82%, from about 60%to about 80%, from about 60% to about 78%, from about 60% to about 76%,from about 60% to about 75%, from about 60% to about 74%, or from about60% to about 72%.

In one or more embodiments, glass layers 12 and/or 20 exhibit an averagetransmittance in the range from about 75% to about 85%, at a thicknessof 0.7 mm or 1 mm, over a wavelength range from about 380 nm to about780 nm. In some embodiments, the average transmittance at this thicknessand over this wavelength range may be in a range from about 75% to about84%, from about 75% to about 83%, from about 75% to about 82%, fromabout 75% to about 81%, from about 75% to about 80%, from about 76% toabout 85%, from about 77% to about 85%, from about 78% to about 85%,from about 79% to about 85%, or from about 80% to about 85%. In one ormore embodiments, glass layers 12 and/or 20 exhibits T_(uv-380) orT_(uv-400) of 50% or less (e.g., 49% or less, 48% or less, 45% or less,40% or less, 30% or less, 25% or less, 23% or less, 20% or less, or 15%or less), at a thickness of 0.7 mm or 1 mm, over a wavelength range fromabout 300 nm to about 400 nm.

In one or more embodiments, glass layers 12 and/or 20 may bestrengthened to include compressive stress that extends from a surfaceto a depth of compression (DOC). The compressive stress regions arebalanced by a central portion exhibiting a tensile stress. At the DOC,the stress crosses from a positive (compressive) stress to a negative(tensile) stress.

In one or more embodiments, glass layers 12 and/or 20 may bestrengthened mechanically by utilizing a mismatch of the coefficient ofthermal expansion between portions of the article to create acompressive stress region and a central region exhibiting a tensilestress. In some embodiments, the glass article may be strengthenedthermally by heating the glass to a temperature below the glasstransition point and then rapidly quenching.

In one or more embodiments, glass layers 12 and/or 20 may be chemicallystrengthened by ion exchange. In the ion exchange process, ions at ornear the surface of glass layers 12 and/or 20 are replaced by—orexchanged with—larger ions having the same valence or oxidation state.In those embodiments in which glass layers 12 and/or 20 comprises analkali aluminosilicate glass, ions in the surface layer of the articleand the larger ions are monovalent alkali metal cations, such as Li⁺,Na⁺, K⁺, Rb⁺, and Cs⁺. Alternatively, monovalent cations in the surfacelayer may be replaced with monovalent cations other than alkali metalcations, such as Ag⁺ or the like. In such embodiments, the monovalentions (or cations) exchanged into glass layers 12 and/or 20 generate astress.

-   -   Aspect (1) of this disclosure pertains to a method of estimating        cold-formability of a complexly curved glass laminate article        comprising a first glass sheet and a second glass sheet, the        method comprising: obtaining a first geometric parameter (G1)        and a second geometric parameter (G2) of a complexly curved        first glass sheet of the glass laminate article; calculating a        cold-forming estimator (CFE) value related to stress experienced        by the first glass sheet during cold-forming, where the CFE        value comprises: B1*G1+B2*G2, wherein B1 and B2 are coefficients        calculated to relate G1 and G2 to the CFE value; and comparing        the calculated CFE value to a cold-forming threshold related to        the probability that defects are formed in the complexly curved        glass laminate article during cold-forming.    -   Aspect (2) pertains to the method of Aspect (1), further        comprising determining that the curved glass laminate article is        suitable for cold-forming, when the calculated CFE value is less        than the cold-forming threshold.    -   Aspect (3) pertains to the method of Aspect (1) or Aspect (2),        wherein the first glass sheet has an average thickness that is        greater than an average thickness of the second glass sheet, and        the first glass sheet is formed from a first glass composition        different from a second glass composition of the second glass        sheet.    -   Aspect (4) pertains to the method of Aspect (3), wherein B1, B2        and the cold-forming threshold are functions of the first glass        composition.    -   Aspect (5) pertains to the method of Aspect (3), wherein the        first glass composition is soda-lime glass.    -   Aspect (6) pertains to the method of Aspect (5), wherein the        first glass sheet is an unstrengthened glass sheet and the        cold-forming threshold is 20 MPa, and further comprising        determining that the curved glass laminate article is suitable        for cold-forming, when the calculated CFE value is less than the        20 MPa.    -   Aspect (7) pertains to the method of Aspect (5), wherein the        first glass sheet is a thermally strengthened glass sheet and        the cold-forming threshold is 50 MPa, and further comprising        determining that the curved glass laminate article is suitable        for cold-forming, when the calculated CFE value is less than the        50 MPa.    -   Aspect (8) pertains to the method of any one of Aspects (2)        through (7), wherein the second glass composition is an alkali        aluminosilicate glass composition or an alkali        aluminoborosilicate glass composition.    -   Aspect (9) pertains to the method of any one of Aspects (2)        through (8), further comprising determining B1 and B2 via        multiple linear regression analyses of finite element        analysis-determined stresses of multiple complexly curved glass        laminate articles.    -   Aspect (10) pertains to the method of any one of Aspects (1)        through (9), wherein the cold-forming threshold is a maximum        allowable stress for the first glass sheet determined by        comparing laminated test samples to stress levels predicted        using finite element analysis.    -   Aspect (11) pertains to the method of any one of Aspects (1)        through (10), wherein the first glass sheet comprises a length,        L, a width, W, and a chord height, wherein G1=L/W, G2=the chord        height, B1=1 and B2=0.5    -   Aspect (12) pertains to the method of any one of Aspects (1)        through (10), wherein the first glass sheet further comprises:        an inner surface; an outer surface opposite the inner surface; a        width, W; a length, L; an average thickness, T1; wherein the        complex curved shape has a chord height, CH, a depth of bend        (DOB), a minimum primary radius of curvature, R1, a secondary        minimum radius of curvature, R2, and a maximum Gaussian        curvature, GC; wherein the second glass layer further comprises:        an inner surface; an outer surface; and an average thickness,        T2; wherein        (0.05673*W−0.1035*L−0.0031*DOB+6.99003*CH+0.1855*R1+0.00115*R2+4.633988*GC−0.1836*T1−101.95*T2)        is less than the cold-forming threshold.    -   Aspect (13) pertains to a method of cold-forming a complexly        curved glass laminate article, comprising: supporting a first        glass sheet, the first sheet of glass material having a        complexly curved shape, a first major surface and a second major        surface; supporting a second glass sheet on the first glass        sheet, wherein the second glass sheet has a first major surface,        a second major surface and a shape that is different from the        complexly curved shape; positioning a polymer interlayer        material between the second major surface of the first glass        sheet and a first major surface of the second glass sheet;        bending the second sheet of glass material into conformity with        the complexly curved shape of the first sheet of glass material,        wherein, during bending, a maximum temperature of the first        glass sheet is less than a glass transition temperature of a        glass material of the first glass sheet, wherein a maximum        temperature of the second glass sheet is less than a glass        transition temperature of a glass material of the second glass        sheet; wherein the complexly curved shape has a first geometric        parameter (G1) and a second geometric parameter (G2), wherein        the first principle stress experienced by the first glass sheet        during bending is less than or equal to an estimated stress        value of (B1*G1+B2*G2), wherein B1 and B2 are coefficients        determined to relate G1 and G2 to the stress experienced by the        first glass sheet during bending.    -   Aspect (14) pertains to the method of Aspect (13), wherein the        first glass sheet has an average thickness that is greater than        an average thickness of the second glass sheet, and the glass        material of the first glass sheet is different from the glass        material of the second glass sheet.    -   Aspect (15) pertains to the method of Aspect (13) or Aspect        (14), wherein the first glass sheet is an unstrengthened glass        sheet and the estimated stress value is less than 20 MPa.    -   Aspect (16) pertains to the method of Aspect (13) or Aspect        (14), wherein the first glass sheet is a thermally strengthened        glass sheet and the estimated stress value is 50 MPa.    -   Aspect (17) pertains to the method of any one of Aspects (13)        through (16), wherein the glass material of the second glass        sheet is an alkali aluminosilicate glass composition or an        alkali aluminoborosilicate glass composition and the glass        material of the first glass sheet is a soda-lime composition.    -   Aspect (18) pertains to a cold-formed glass laminate article        comprising: a first glass layer comprising: an inner surface; an        outer surface opposite the inner surface; a width, W; a length,        L; a complex curved shape having a chord height, CH, wherein        −0.14<L/W−0.05*(CH)<0.223; and a second glass layer comprising:        an inner surface; an outer surface; a polymer interlayer        disposed between the inner surface of the first glass layer and        inner surface of the second glass layer.    -   Aspect (19) pertains to the cold-formed glass laminate article        of Aspect (18), wherein the first glass layer has an average        thickness, T1, that is greater than an average thickness, T2, of        the second glass layer.    -   Aspect (20) pertains to the cold-formed glass laminate article        of Aspect (19), wherein T1 is between 1 mm and 4 mm, and T2 is        between 0.3 mm and 1 mm.    -   Aspect (21) pertains to the cold-formed glass laminate article        of any one of Aspects (18) through (20), wherein W is between        300 mm and 1800 mm, L is between 230 mm and 1600 mm, and CH is        between 1 mm and 45 mm.    -   Aspect (22) pertains to the cold-formed glass laminate article        of any one of Aspects (18) through (21), wherein a glass        material of the first glass layer is different from a glass        material of the second glass layer.    -   Aspect (23) pertains to the cold-formed glass laminate article        of Aspect (22), wherein the glass material of the second glass        layer is an alkali aluminosilicate glass composition or an        alkali aluminoborosilicate glass composition and the glass        material of the first glass sheet is a soda-lime composition.    -   Aspect (24) pertains to the cold-formed glass laminate article        of any one of Aspects (18) through (23), wherein the second        glass layer is a chemically strengthened glass material.    -   Aspect (25) pertains to a cold-formed glass laminate article        comprising: a first glass layer comprising: an inner surface; an        outer surface opposite the inner surface; a width, W; a length,        L; an average thickness, T1; a complex curved shape having a        chord height, CH, a depth of bend (DOB), a minimum primary        radius of curvature, R1, a secondary minimum radius of        curvature, R2, and a maximum Gaussian curvature, GC; a second        glass layer comprising: an inner surface; an outer surface; and        an average thickness, T2; and an interlayer disposed between the        inner surface of the first glass layer and inner surface of the        second glass layer; wherein        (0.05673*W−0.1035*L−0.0031*DOB+6.99003*CH+0.1855*R1+0.00115*R2+4.633988*GC−0.1836*T1−101.95*T2)        is less than 80 MPa.    -   Aspect (26) pertains to the cold-formed glass laminate article        of Aspect (25), wherein T1 is greater than an T2.    -   Aspect (27) pertains to the cold-formed glass laminate article        of Aspect (25) or Aspect (26), wherein T1 is between 1 mm and 4        mm, and T2 is between 0.3 mm and 1 mm.    -   Aspect (28) pertains to the cold-formed glass laminate article        of any one of Aspects (25) through (27), wherein, W is between        300 mm and 1800 mm, L is between 230 mm and 1600 mm, CH is        between 1 mm and 45 mm, DOB is between 5 mm and 210 mm, R1 is        between 40 mm and 5000 mm, R2 is between 740 mm and 32500 mm,        and GC is between 0.14×10⁻⁷ 1/mm² and 15×10⁻⁷ 1/mm².    -   Aspect (29) pertains to the cold-formed glass laminate article        of any one of Aspects (25) through (28), wherein a glass        material of the first glass layer is different from a glass        material of the second glass layer.    -   Aspect (30) pertains to the cold-formed glass laminate article        of Aspect (29), wherein the glass material of the second glass        layer is an alkali aluminosilicate glass composition or an        alkali aluminoborosilicate glass composition and the glass        material of the first glass sheet is a soda-lime composition.    -   Aspect (31) pertains to the cold-formed glass laminate article        of any one of Aspects (25) through (30), wherein the second        glass layer is a chemically strengthened glass material.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is in no way intendedthat any particular order be inferred. In addition, as used herein, thearticle “a” is intended to include one or more than one component orelement, and is not intended to be construed as meaning only one.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the disclosed embodiments. Since modifications,combinations, sub-combinations and variations of the disclosedembodiments incorporating the spirit and substance of the embodimentsmay occur to persons skilled in the art, the disclosed embodimentsshould be construed to include everything within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A cold-formed roof for a vehicle comprising: afirst glass layer comprising a length, L, a width, W, an averagethickness, T1, a complex curved shape having a non-zero chord height,CH, a non-zero depth of bend (DOB), a non-zero minimum primary radius ofcurvature, R1, a non-zero secondary minimum radius of curvature, R2, anda non-zero maximum Gaussian curvature, GC; a second glass layercomprising an average thickness, T2; and an interlayer disposed betweenthe inner surface of the first glass layer and inner surface of thesecond glass layer; wherein: (0.05673 MPa/mm*W−0.1035 MPa/mm*L−0.0031MPa/mm*DOB+6.99003 MPa/mm*CH+0.01855 MPa/mm*R1+0.00115MPa/mm*R2+4.633988 MPa*mm²*10⁷*GC−0.1836 MPa/mm*T1−101.95 MPa/mm*T2) isless than 80 MPa, W is greater than or equal to 300 mm and less than orequal to 1800 mm, L is greater than or equal to 230 mm and less than orequal to 1600 mm, L/W is greater than 0 and less than or equal to 1.0,DOB is greater than or equal to 5.0 mm and less than or equal to 210 mm,CH is greater than or equal to 1 mm and less than or equal to 45 mm, andthe first glass layer is hot-formed to have the complex shape and thesecond glass layer is cold-formed against the first glass layer at atemperature beneath a softening temperature of the second glass layer topossess the complex curved shape.
 2. The cold-formed roof of claim 1,wherein T1 is at least 2.5 times T2.
 3. The cold-formed roof of claim 2,wherein T1 is greater than or equal to 1.5 mm and less than or equal to4.0 mm.
 4. The cold-formed roof of claim 3, wherein T2 is greater thanor equal to 0.3 mm and less than or equal to 1.0 mm.
 5. The cold-formedroof of claim 1, wherein: the first glass layer is formed of a firstglass composition and the second glass layer is formed of a second glasscomposition that is different from the first glass composition the firstcomposition is a soda lime glass and the second composition is an alkalialuminosilicate glass composition or an alkali aluminoborosilicate glasscomposition, the second composition is chemically strengthened, and thesecond glass layer comprises a depth of compression in a range that isgreater than or equal to 30 μm and less than or equal to 90 μm and amaximum surface compressive stress that is greater than or equal to 300MPa and less than or equal to 1000 MPa.
 6. The cold-formed roof of claim1, wherein, 0.14×10⁻⁷ 1/mm²≤GC≤15×10⁻⁷ 1/mm².
 7. The cold-formed roof ofclaim 6, wherein 0.05673 MPa/mm*W−0.1035 MPa/mm*L−0.0031MPa/mm*DOB+6.99003 MPa/mm*CH+0.01855 MPa/mm*R1+0.00115MPa/mm*R2+4.633988 MPa*mm²*10⁷*GC−0.1836 MPa/mm*T1−101.95 MPa/mm*T2) isless than 50 MPa.
 8. The cold-formed roof of claim 6, wherein 0.05673MPa/mm*W−0.1035 MPa/mm*L−0.0031 MPa/mm*DOB+6.99003 MPa/mm*CH+0.01855MPa/mm*R1+0.00115 MPa/mm*R2+4.633988 MPa*mm²*10⁷*GC−0.1836MPa/mm*T1−101.95 MPa/mm*T2) is less than 20 MPa.
 9. The cold-formed roofof claim 1, wherein the DOB is a maximum depth of a surface of the firstglass layer from a flat projection plane of the first glass layer,wherein the CH is a maximum distance between a center line chord of thefirst glass layer and an arc of the first glass layer measured in adirection perpendicular to a direction in which the DOB is measured. 10.The cold-formed roof of claim 9, wherein the chord height is at an edgeof the cold-formed roof.
 11. The cold-formed roof of claim 1, whereinthe second glass layer is planar prior to being cold-formed against thefirst glass layer.